A computational study of viscous dissipation and entropy generation in unsteady pipe flow

Abstract

Numerical simulations of transient entropy generation in a reservoir-pipe-valve system are presented. The flow transient is initiated through sudden closure of the downstream valve. An unsteady two-dimensional water hammer model is adopted. Time integration is performed using the classical fourth-order Runge–Kutta method while the spatial terms are discretized using central difference expressions. Entropy generation is shown to depend on a non-dimensional parameter representing the ratio of the viscous diffusion time scale to the pipe period. For small values of the non-dimensional parameter, entropy generation is rapidly attenuated from its steady-state value to zero while for large values, entropy generation persists for a much longer time. Moreover, for large values of the non-dimensional parameter, excessive entropy generation rates are realized during the transient which are several orders of magnitude higher than the steady-state rate. Such a behavior is attributed to elevated transient shear stress values in the near wall region which result in excessive viscous dissipation and hence higher entropy generation rates. Finally, it is shown that during the transient, the location of maximum entropy generation is no longer restricted to the pipe wall.